How many 4 digit palindromes less than 5000?

Answer 1

While I'm tempted to tell you to do your own homework, this is intriguing enough that I'm willing to spend some time helping you to work it out.

First: by four digit palindromes that means numbers of the form ABBA.
A is constrained by "less than 5000". A can only be 0, 1, 2, 3, or 4, because otherwise ABBA would be greater than 5000 (the lowest possible ABBA number where A is 5 or greater is 5005 ... which is over 5000).
A is further constrained by "4 digit". It can't be 0, because by convention we don't write leading zeroes and then ABBA would only be a three digit number.
So A can be 1, 2, 3, or 4 (4 distinct possibilities).
There are no constraints on B. It can be any digit (including 0), which means there are 10 distinct possibilities.

Since once we specify both A and B we're done, that means there are (4 possibilities for A) x (10 possibilities for B) = 40 four-digit palindromes less than 5000.